Published March 13, 2026 | Version v2
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Interaction Dependent Deformation Parameters: Reconciling Generalized Uncertainty Principles with Multi-Messenger Constraints

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Standard Generalized Uncertainty Principle (GUP) models with a universal deformation parameter ($\beta \sim 1$) are under increasing tension from precision Gamma-Ray Burst (GRB) and LHAASO observations. We propose a phenomenological ansatz where the deformation parameter scales with the square of the interaction coupling: $\beta_i \propto \alpha_i^2$. We demonstrate that this hierarchy ($\beta_\gamma \ll \beta_\nu \ll \beta_{hadron}$) naturally satisfies all current multi-messenger constraints, including the tight bounds from GRB 221009A and the Crab Nebula PeVatron, without invoking arbitrary scales. Crucially, the framework breaks the degeneracy of universal models by predicting a species-dependent time delay hierarchy ($\Delta t_\nu > \Delta t_\gamma$) with a fixed ratio determined by Standard Model couplings: $\Delta t_\nu / \Delta t_\gamma \approx (\alpha_W / \alpha_{EM})^2 \approx 21.5$. This mechanism resurrects the parameter space for Linear ($n=1$) quantum gravity models, predicting macroscopic ($\sim 10$ s) delays for PeV neutrinos that are falsifiable with current generation detectors.

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